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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Analysis of a Prey-predator Model with Prey Refuge in Infected Prey and Strong Allee Effect in Susceptible Prey Population

Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 671--703 | DOI:10.5890/DNC.2022.12.008

Sangeeta Saha$^{1}$, Alakes Maiti$^{2}$, Guruprasad Samanta$^{1}$

$^{1}$ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah - 711103, India

$^{2}$ Department of Mathematics, Vidyasagar Evening College, Kolkata-700006, India

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Abstract

An eco-epidemiological predator-prey model with Holling type-II functional response is proposed in this work. In the presence of disease, the prey population has been divided into two subpopulations: susceptible and infected prey. The predator can access the full healthy prey population for hunting but a predator is provided with a fraction of the infected prey as infected prey refuge term is incorporated here. Also, a strong Allee effect in susceptible population is introduced to make the model more realistic. Boundedness and positivity of the system strengthen that the proposed model is well-posed. The strong Allee threshold and the infected refuge parameter have been taken as the key parameters to control the system dynamics. The numerical simulation gives that regulating the refuge parameter can turn an oscillating state into a stable coexistence state. Also, the system changes its dynamics from two interior equilibrium points to no interior point when this refuge parameter crosses the saddle-node bifurcation threshold. Besides, the strong Allee threshold can also change the dynamics of a system from oscillating state to steady-state through Hopf bifurcation.

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